Problem: The grades on a physics midterm at Gardner Bullis are normally distributed with $\mu = 67$ and $\sigma = 5.5$. Vanessa earned a n $84$ on the exam. Find the z-score for Vanessa's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Vanessa's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{84 - {67}}{{5.5}}} $ ${ z \approx 3.09}$ The z-score is $3.09$. In other words, Vanessa's score was $3.09$ standard deviations above the mean.